EXERCISE 7-29 (CONTINUED)
5. Target net income:
$65,000 $48,750
Sales volume required to earn target net income of $48,750
$162.50
700 bicycles
This means that the shop will need to sell the following volume of each type of
bicycle to earn the target net income:
High-quality ............................................................................ 175 (700 .25)
Medium-quality ...................................................................... 525 (700 .75)
SOLUTIONS TO PROBLEMS
PROBLEM 7-36 (30 MINUTES)
1. Unit contribution margin:
Sales price………………………………… $64.00
Less variable costs:
Sales commissions ($64 x 5%)…… $ 3.20
System variable costs……………… 16.00 19.20
Unit contribution margin……………….. $44.80
Break-even point = fixed costs ÷ unit contribution margin
= $985,600 ÷ $44.80
= 22,000 units
2. Model no. 4399 is more profitable when sales and production average 46,000 units.
Model Model
No. 6754 No. 4399
Sales revenue (46,000 units x $64.00)……... $2,944,000 $2,944,000
Less variable costs:
Sales commissions ($2,944,000 x 5%)… $ 147,200 $ 147,200
System variable costs:……………………
46,000 units x $16.00…………………. 736,000
46,000 units x $12.80…………………. 588,800
7-5
Total variable costs……………………….. $ 883,200 $ 736,000
Contribution margin…………………………... $2,060,800 $2,208,000
Less: Annual fixed costs…………………….. 985,600 1,113,600
Net income……………………………………… $1,075,200 $1,094,400
3. Annual fixed costs will increase by $90,000 ($450,000 ÷ 5 years) because of straight-
line depreciation associated with the new equipment, to $1,203,600 ($1,113,600 +
$90,000). The unit contribution margin is $48 ($2,208,000 ÷ 46,000 units). Thus:
Required sales = (fixed costs + target net profit) ÷ unit contribution margin
= ($1,203,600 + $956,400) ÷ $48
= 45,000 units
4. Let X = volume level at which annual total costs are equal
$16.00X + $985,600 = $12.80X + $1,113,600
$3.20X = $128,000
X = 40,000 units
PROBLEM 7-37 (35 MINUTES)
1. Current income:
Sales revenue………………………... $3,360,000
Less: Variable costs………………… $ 840,000
Fixed costs……………………. 2,280,000 3,120,000
Net income……………………………. $ 240,000
Advanced Electronics has a contribution margin of $60 [($3,360,000 - $840,000) ÷
42,000 sets] and desires to increase income to $480,000 ($240,000 x 2). In addition,
the current selling price is $80 ($3,360,000 ÷ 42,000 sets). Thus:
Required sales = (fixed costs + target net profit) ÷ unit contribution margin
= ($2,280,000 + $480,000) ÷ $60
= 46,000 sets, or $3,680,000 (46,000 sets x $80)
2. If operations are shifted to Mexico, the new unit contribution margin will be $62 ($80 -
$18). Thus:
Break-even point = fixed costs ÷ unit contribution margin
= $1,984,000 ÷ $62
= 32,000 units
7-6
3. (a) Advanced Electronics desires to have a 32,000-unit break-even point with a
$60 unit contribution margin. Fixed cost must therefore drop by $360,000
($2,280,000 - $1,920,000), as follows:
Let X = fixed costs
X ÷ $60 = 32,000 units
X = $1,920,000
(b) As the following calculations show, Advanced Electronics will have to
generate a contribution margin of $71.25 to produce a 32,000-unit break-even
point. Based on an $80.00 selling price, this means that the company can
incur variable costs of only $8.75 per unit. Given the current variable cost of
$20.00 ($80.00 - $60.00), a decrease of $11.25 per unit ($20.00 - $8.75) is
needed.
Let X = unit contribution margin
$2,280,000 ÷ X = 32,000 units
X = $71.25
4. (a) Increase
(b) No effect
(c) Increase
(d) No effect
PROBLEM 7-39 (35 MINUTES)
1. Plan A break-even point = fixed costs ÷ unit contribution margin
= $22,000 ÷ $22*
= 1,000 units
Plan B break-even point = fixed costs ÷ unit contribution margin
= $66,000 ÷ $30**
= 2,200 units
* $80 - [($80 x 10%) + $50]
** $80 - $50
7-7
1. Operating leverage refers to the use of fixed costs in an organization’s overall cost
structure. An organization that has a relatively high proportion of fixed costs and
low proportion of variable costs has a high degree of operating leverage.
2. Calculation of contribution margin and profit at 6,000 units of sales:
Plan A Plan B
Sales revenue: 6,000 units x $80………………. $480,000 $480,000
Less variable costs:
Cost of purchasing product:
6,000 units x $50…………………….…… $300,000 $300,000
Sales commissions: $480,000 x 10%……... 48,000 ----
Total variable cost……………………….. $348,000 $300,000
Contribution margin……………………………… $132,000 $180,000
Fixed costs…………………………………………. 22,000 66,000
Net income…………………………………………. $110,000 $114,000
Operating leverage factor = contribution margin ÷ net income
Plan A: $132,000 ÷ $110,000 = 1.2
Plan B: $180,000 ÷ $114,000 = 1.58 (rounded)
Plan B has the higher operating leverage factor.
4 & 5. Calculation of profit at 5,000 units:
Plan A Plan B
Sales revenue: 5,000 units x $80………………. $400,000 $400,000
Less variable costs:
Cost of purchasing product:
5,000 units x $50………………………….. $250,000 $250,000
Sales commissions: $400,000 x 10%……... 40,000 ----
Total variable cost……………………….. $290,000 $250,000
Contribution margin……………………………… $110,000 $150,000
Fixed costs………………………………………… 22,000 66,000
Net income…………………………………………. $ 88,000 $ 84,000
Plan A profitability decrease:
$110,000 - $88,000 = $22,000; $22,000 ÷ $110,000 = 20%
7-8
Plan B profitability decrease:
$114,000 - $84,000 = $30,000; $30,000 ÷ $114,000 = 26.3% (rounded)
Consolidated would experience a larger percentage decrease in income if it adopts
Plan B. This situation arises because Plan B has a higher degree of operating
leverage. Stated differently, Plan B’s cost structure produces a greater percentage
decline in profitability from the drop-off in sales revenue.
Note: The percentage decreases in profitability can be computed by multiplying the
percentage decrease in sales revenue by the operating leverage factor. Sales
dropped from 6,000 units to 5,000 units, or 16.67%. Thus:
Plan A: 16.67% x 1.2 = 20.0%
Plan B: 16.67% x 1.58 = 26.3% (rounded)
6. Heavily automated manufacturers have sizable investments in plant and equipment,
along with a high percentage of fixed costs in their cost structures. As a result,
there is a high degree of operating leverage.
In a severe economic downturn, these firms typically suffer a significant
decrease in profitability. Such firms would be a more risky investment when
compared with firms that have a low degree of operating leverage. Of course, when
times are good, increases in sales would tend to have a very favorable effect on
earnings in a company with high operating leverage.
PROBLEM 7-44 (45 MINUTES)
1. Break-even point in units:
fixed costs
Break-even point
unit contribution margin
Calculation of contribution margins:
Computer-Assisted Labor-Intensive
Manufacturing System Production System
Selling price ...................................... $30.00 $30.00
Variable costs:
Direct material .............................. $5.00 $5.60
Direct labor ................................... 6.00 7.20
Variable overhead ........................ 3.00 4.80
Variable selling cost .................... 2.00 16.00 2.00 19.60
Contribution margin per unit $14.00 $10.40
7-9
